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Short-Term Depression and Facilitation

Overview

Synapses can change strength through a pulse train even with fixed anatomy. The examples in chapter39.ipynb first introduce a smooth spike/pulse approximation motivating synaptic gating, then show depressing and facilitating synapses in RTM and WB neurons.

Core ideas

Depression depletes available resources after release and recovers between events. Facilitation transiently increases utilization, so a pulse sequence can initially grow. Their balance changes effective synaptic conductance, postsynaptic timing, and whether early or late pulses evoke spikes.

Essential model

With resources $x$ and utilization $u$, release is proportional to $ux$; depression lowers $x$ after events and facilitation raises $u$. The resulting synaptic gate enters the conductance current $gs(E_{\rm rev}-v)$. The introductory smooth proxy is $\gamma=1+\tanh(v/10)$, which approximates a spike-shaped pulse for a voltage trace.

Code examples

All four examples live in one notebook, chapter39.ipynb.

simulate_pulses/plot_pulses cover PULSES: an RTM voltage trace and its smooth $\gamma=1+\tanh(v/10)$ spike/pulse approximation, including its per-spike area calculation, with i_ext exposed through an interact() slider.

simulate_rtm_depressing_facilitating/plot_rtm_depressing_facilitating cover RTM_WITH_DEPRESSING_AND_FACILITATING_S, comparing depression and facilitation together in an RTM cell, with tau_facil exposed through a slider.

simulate_rtm_depressing/plot_rtm_depressing cover RTM_WITH_DEPRESSING_S, depression alone in an RTM cell, with U and tau_rec exposed through sliders.

simulate_wb_with_depressing_s/plot_wb_with_depressing_s cover WB_WITH_DEPRESSING_S, the depressing-synapse case for a WB cell (integrated with an explicit Heun/RK2 step rather than odeint), with U and C exposed through sliders.

What to look for

In PULSES, compare the voltage crossing with the smooth $\gamma$ pulse; it is not a resource/utilization simulation. In the remaining examples, track synaptic strength over events: depression should weaken later events until recovery, while facilitation can enhance them transiently. Compare RTM and WB to separate synaptic from intrinsic-neuron effects.

Suggested order

  1. Run PULSES to see the smooth spike/pulse approximation.
  2. Compare the depressing RTM and WB examples.
  3. Run the RTM depression-plus-facilitation comparison.

Prerequisites and related chapters

Chapter 20 supplies the chemical-synapse gate, Chapter 5 RTM and WB cells, and Chapter 40 spike-timing-dependent plasticity.

Running the examples

Open chapter39.ipynb and run the cells top to bottom. NumPy, SciPy, Matplotlib, and ipywidgets are required.